How much is it favoured? Quite a lot. The relevant clashes are shown below. The ''cis'' case is shown for comparison purposes, but is less important here because the two ring-flipped conformations have the same clashes. For the ''trans'' isomers the clashes are a mix of 1,3-diaxial interactions and gauche methyl clashes. The diequatorial conformation is favoured by over 11 kJ mol<sup>-1</sup>.

How much is it favoured? Quite a lot. The relevant clashes are shown below. The ''cis'' case is shown for comparison purposes, but is less important here because the two ring-flipped conformations have the same clashes. For the ''trans'' isomers the clashes are a mix of 1,3-diaxial interactions and gauche methyl clashes. The diequatorial conformation is favoured by over 11 kJ mol<sup>-1</sup>.

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[[Image:DiMeCx Costs.png|thumb|center|700px| '''Scheme 4:''' The Energetic Costs of Various Clashes in ''cis'' and ''trans'' 1,2-Dimethylcyclohexane]]

+

[[Image:DiMeCx Costs 2.png|thumb|center|700px| '''Scheme 4:''' The Energetic Costs of Various Clashes in ''cis'' and ''trans'' 1,2-Dimethylcyclohexane]]

Assuming equilibrium at room temperature, and remembering that ΔE = -RTlnK, we can generate a curve a little like this one:

Assuming equilibrium at room temperature, and remembering that ΔE = -RTlnK, we can generate a curve a little like this one:

Chem3x11 Lecture 3

Key concepts

The preferred conformation of a substituted cyclohexane depends on what's attached to it

Two cyclohexanes can be fused to give decalins

Attachment of substituents to cyclohexanes can lock their conformations, giving complex, but very information-rich NMR spectra

Cyclohexanes with Two Substituents

cis and trans refer to Relative Stereochemistry. Nothing to do with Ring Flipping

We need to be clear on one thing from the outset. cis and trans isomers do not interconvert - they are separate structures that are configurational isomers (diastereomers). It's not like you can convert one to the other with a ring flip. Here are the cis and trans isomers of 1,2-dimethylcyclohexane.

Scheme 1:cis and trans Diastereomers of 1,2-Dimethylcyclohexane

Drawings like this allow us to see relative stereochemistry of those methyl groups, but we need to be happy thinking about the rings in 3D so we can think about what the preferred conformations might be. The easiest way to do this is to draw a cyclohexane ring, draw in one substituent, then draw in the other given the relative stereochemistry. Then perform a ring flip to get the other conformation. Here are the conformations for the cis isomer.

Scheme 2: Conformations of the cis Diastereomers of 1,2-Dimethylcyclohexane

In both cases one methyl is equatorial and one is axial. Both conformations are of the same energy. The trans isomer is different. In one conformation the methyls are both equatorial, and in the other they are both axial. Clearly these conformations will have different energies and the di-equatorial conformation is going to be favoured.

Scheme 3: Conformations of the trans Diastereomers of 1,2-Dimethylcyclohexane

How much is it favoured? Quite a lot. The relevant clashes are shown below. The cis case is shown for comparison purposes, but is less important here because the two ring-flipped conformations have the same clashes. For the trans isomers the clashes are a mix of 1,3-diaxial interactions and gauche methyl clashes. The diequatorial conformation is favoured by over 11 kJ mol-1.

Scheme 4: The Energetic Costs of Various Clashes in cis and trans 1,2-Dimethylcyclohexane

Assuming equilibrium at room temperature, and remembering that ΔE = -RTlnK, we can generate a curve a little like this one:

Scheme 5: Proportion of Isomers at Equilibrium as a Function of the Energy Difference Between Them

...which shows that the diequatorial conformation is massively favoured under normal circumstances. We can't forget about the diaxial conformation. It's still there, just not very common.

Chirality of 1,2-Dimethylcyclohexane

Look at the two chair conformations of cis-1,2-dimethylcyclohexane. They're enantiomers. Does that mean this compound is chiral? No - the two conformations interconvert rapidly under normal conditions and we can't separate them. Incidentally they interconvert via a meso boat form.

Scheme 6:cis-1,2-Dimethylcyclohexane is "Achiral"

It's easier to see that the cis isomer is achiral with the 2D diagram, because there's an obvious plane of symmetry running through the molecule, but it's important also to be able to reach the same conclusion using a more grown-up 3D analysis of the molecule.

What about the trans isomer? Much more interesting. It's chiral, no matter what you do. Take the 2D drawing, draw the enantiomer. They're not the same. Further, when you draw the 3D conformation, and ring-flip, the ring-flipped conformations are not the same, nor are they enantiomers. This molecule is chiral, no matter what shape it adopts.

Decalins

Again, we can have cis and trans isomers that do not interconvert, no matter how much ring flipping etc you try to do.

Scheme 11:cis and trans Decalins Don't Interconvert

Drawing the preferred conformation of the trans fused system is straightforward. Both rings are chairs. The small Hs go axial, leaving the bulkier carbon chains to be equatorial.

Scheme 12: Drawing trans-Decalin

(but actually you can't do ring flipping in this compound - can you see why?)

Drawing the cis can give people nightmares, but stay calm and you'll be fine. Draw one ring. Take the two leftmost carbons and draw an axial C-C bond down and an equatorial C-C bond. That starts you on the second ring, which then also needs to come out chair-like, and it's often easier to draw that in if you rotate your page (or your mind, or both) to see that second ring as a chair.

Scheme 13: Drawing cis-Decalin

Why do we care about decalins? One of the most important classes of natural molecules, the steroids, have these structures in them. They are synthesised by an extraordinarily cool reaction, and the resulting shape of the molecule is partly determined by the fact that these trans ring junctions are a little more stable than the cis, all other things being equal. Look at the following structures to see if you are happy that the 2D drawings imply the 3D structures and vice versa.

Scheme 14: Decalins Occur in Steroids

1H NMR Spectra of Substituted Cyclohexanes

In cyclohexane there is rapid ring-flipping that interconverts axial and equatorial protons so a single averaged peak is observed in the 1H NMR spectra - i.e. we don't observe the "isolated" conformations and the NMR spectra are simpler than we might expect. If we cool our sample a lot, we should be able to slow down the interconversion. So as the temperature goes down, our signals might broaden, and then at a sufficiently low temperature we might start to see separate signals for axial and equatorial protons.

For simply substituted cyclohexanes, where there is substantial movement of the molecule, we see chemical shifts and coupling constants that are a weighted average of those for all conformations of the molecule. If, however, the conformation is "locked" by big substituent, or if ring flipping is somehow prevented (e.g. in a trans-decalin system) then we start to see detailed coupling constants for individual protons arising from a single conformation.

The coupling constants we see in a molecule's 1H NMR spectra reveal a fair amount about its molecular structure, because the size of the J value depends on how well the relevant orbitals are overlapping.

Scheme 15: Coupling Constants Depend on the Geometry of Orbital Overlap, i.e. the Dihedral Angle Between the Bonds

In cyclohexanes where we can see such detail, the J value for a coupling between two axial protons is large, with the other possible geometries giving rise to much smaller coupling constants.